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Kamyar Azizzadenesheli | Anima Anandkumar | Kaushik Bhattacharya | Zongyi Li | Nikola Kovachki | Andrew Stuart | Burigede Liu
[1] L. F. Mingo,et al. FOURIER NEURAL NETWORKS: AN APPROACH WITH SINUSOIDAL ACTIVATION FUNCTIONS 1 , 2003 .
[2] E Weinan,et al. The Deep Ritz Method: A Deep Learning-Based Numerical Algorithm for Solving Variational Problems , 2017, Communications in Mathematics and Statistics.
[3] Jian Sun,et al. Deep Residual Learning for Image Recognition , 2015, 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR).
[4] Nicholas Zabaras,et al. Bayesian Deep Convolutional Encoder-Decoder Networks for Surrogate Modeling and Uncertainty Quantification , 2018, J. Comput. Phys..
[5] George Em Karniadakis,et al. DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators , 2019, ArXiv.
[6] Yann LeCun,et al. Fast Training of Convolutional Networks through FFTs , 2013, ICLR.
[7] Lexing Ying,et al. Solving parametric PDE problems with artificial neural networks , 2017, European Journal of Applied Mathematics.
[8] Kamyar Azizzadenesheli,et al. EikoNet: Solving the Eikonal Equation With Deep Neural Networks , 2021, IEEE Transactions on Geoscience and Remote Sensing.
[9] Paris Perdikaris,et al. Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations , 2019, J. Comput. Phys..
[10] Kurt Hornik,et al. Multilayer feedforward networks are universal approximators , 1989, Neural Networks.
[11] Kamyar Azizzadenesheli,et al. Multipole Graph Neural Operator for Parametric Partial Differential Equations , 2020, NeurIPS.
[12] Kamyar Azizzadenesheli,et al. Neural Operator: Graph Kernel Network for Partial Differential Equations , 2020, ICLR 2020.
[13] Wei Li,et al. Convolutional Neural Networks for Steady Flow Approximation , 2016, KDD.
[14] Thomas Brox,et al. U-Net: Convolutional Networks for Biomedical Image Segmentation , 2015, MICCAI.
[15] Gordon Wetzstein,et al. Implicit Neural Representations with Periodic Activation Functions , 2020, NeurIPS.
[16] Leah Bar,et al. Unsupervised Deep Learning Algorithm for PDE-based Forward and Inverse Problems , 2019, ArXiv.
[17] Jonas Adler,et al. Solving ill-posed inverse problems using iterative deep neural networks , 2017, ArXiv.
[18] Karthik Kashinath,et al. Towards Physics-informed Deep Learning for Turbulent Flow Prediction , 2020, KDD.
[19] Andrew M. Stuart,et al. The Random Feature Model for Input-Output Maps between Banach Spaces , 2021, SIAM J. Sci. Comput..
[20] G. Roberts,et al. MCMC Methods for Functions: ModifyingOld Algorithms to Make Them Faster , 2012, 1202.0709.
[21] Vladimir Vapnik,et al. Statistical learning theory , 1998 .
[22] Ronald A. DeVore,et al. Chapter 3: The Theoretical Foundation of Reduced Basis Methods , 2017 .
[23] Karthik Duraisamy,et al. Prediction of aerodynamic flow fields using convolutional neural networks , 2019, Computational Mechanics.
[24] Andrew M. Stuart,et al. SMAI-JCM SMAI Journal of Computational Mathematics Model Reduction And Neural Networks For Parametric PDEs , 2022 .
[25] Lexing Ying,et al. A Multiscale Neural Network Based on Hierarchical Matrices , 2018, Multiscale Model. Simul..
[26] Lexing Ying,et al. BCR-Net: a neural network based on the nonstandard wavelet form , 2018, J. Comput. Phys..